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The ternary alloy Ag–In–Ce is the only Ce-based quasicrystal approximant showing the heavy fermion feature. Here, we report the physical properties of Ag–In–(CexY1−x). As the Ce concentration x is diluted by the nonmagnetic element Y, the spin glass freezing temperature Tf is progressively suppressed. At T > Tf, the uniform magnetic susceptibility and electronic specific heat coefficient show \(\chi (T,x)^{ - 1} = \alpha [T^{\zeta } + \theta _{\text{eff}}^{\zeta }(x)]\) (where α is a constant, ζ \(\simeq \) 0.7, and θeff is an effective Weiss temperature) and \(C(T,x)/T = \beta \ln [T/T_{0}(x)]\) (where β is a constant and T0 is a characteristic temperature), respectively. Near the critical concentration xc where θeff vanishes, χ and C/T exhibit power-law and logarithmic divergence, respectively, as T → 0. We stress that α, ζ, and β are independent of x, indicating that the Tζ and ln T terms come from local fluctuations that are present everywhere in the x–T phase diagram, regardless of quantum critical point. We argue that the quantum critical behavior is driven by valence fluctuations. [ABSTRACT FROM AUTHOR]